Exercise

# From single to annual premium

Miss Cathleen wants to finance her deferred life annuity with annual premiums payable for 25 years beginning at age 40. But since she plans to reduce her teaching hours from age 55 on, the premium should reduce by one-half after 15 years, as shown in the graph below. What will be the initial premium to be paid by Miss Cathleen?

The variables `kpx`

, `discount_factors`

and `single_premium`

computed in the previous exercise are preloaded.

Instructions

**100 XP**

- Define the premium pattern as
`rho`

. This vector should have the same length as`kpx`

. - Compute and print the
`initial_premium`

by dividing`single_premium`

by the sum of the elementwise multiplication of`rho`

,`discount_factors`

and`kpx`

. - Inspect the annual premiums by printing the product of
`initial_premium`

and`rho`

. - Without taking the time value of money and the mortality into account, compute the total sum that Miss Cathleen has to pay to finance the life annuity.